Simplify the following expression: $\dfrac{7t^4}{2t^5}$ You can assume $t \neq 0$.
Solution: $ \dfrac{7t^4}{2t^5} = \dfrac{7}{2} \cdot \dfrac{t^4}{t^5} $ To simplify $\frac{7}{2}$ , find the greatest common factor (GCD) of $7$ and $2$ $7 = 7$ $2 = 2$ $ \mbox{GCD}(7, 2) = = 1 $ $ \dfrac{7}{2} \cdot \dfrac{t^4}{t^5} = \dfrac{1 \cdot 7}{1 \cdot 2} \cdot \dfrac{t^4}{t^5} $ $\phantom{ \dfrac{7}{2} \cdot \dfrac{4}{5}} = \dfrac{7}{2} \cdot \dfrac{t^4}{t^5} $ $ \dfrac{t^4}{t^5} = \dfrac{t \cdot t \cdot t \cdot t}{t \cdot t \cdot t \cdot t \cdot t} = \dfrac{1}{t} $ $ \dfrac{7}{2} \cdot \dfrac{1}{t} = \dfrac{7}{2t} $